Method of and means for generating gear teeth

ABSTRACT

The invention relates to the generation of tooth surfaces on wormgears, especially wormgears mating with large worms, crowned teeth of gear-coupling hubs, crowned teeth in general, and others. The tool used rotates in timed relation with the workspindle. It may be a hob with a single thread or with a smaller number of threads than the worm of a wormgear pair. Standard hobs may be used to cut wormgears rather than a hob that directly represents the mating worm.

United States Patent Wildhaber METHOD OF AND MEANS FOR GENERATING GEAR TEETH Primary Examiner--Francis S. Husar 5 7] ABSTRACT The invention relates to the generation of tooth surfaces on wormgears, especially wormgears mating with large worms, crowned teeth of gear-coupling hubs, crowned teeth in general, and others. The tool used rotates in timed relation with the work-spindle. It may be a hob with a single thread or with a smaller number of threads than the worm of a wormgear pair. Stan dard hobs may be used to cut wormgears rather than a hob that directly represents the mating worm.

14 Claims, 25 Drawing Figures [76] Inventor: Ernest Wildhaber, 124 Summit Dr.,

Brighton, NY. 14620 [22] Filed: June 5, 1972 [21] Appl. No.: 259,737

[52] U.S. Cl. 90/4 [51] Int. Cl B23f 11/00 [58] Field of Search 90/4 [56] References Cited UNITED STATES PATENTS 2,839,968 6/1958 Moncrieff 90/4 IFIIGJIZ METHOD OF AND MEANS FOR GENERATING GEAR TEETH The relative feed motion is split up into a uniform motion along the axis of the work-spindle, a further translatory motion perpendicular thereto, and into a turning motion about an axis that intersects the angular adjustment axis of the tool and is close to the tool. The last-named two feed components are operated from a pivoted feed member that turns on its axis at such a varying rate that radial adjustment thereon of an eccentric can produce true circular relative motion of any desired radius within machine range, in combination with uniform feed along the work axis. In cutting wormgears a linear motion at a varying rate may be added.

In earlier days it was quite common to employ helical gear pairs to transmit motion between offset axes disposed at right angles. They are convenient and easily produced, but have inferior tooth contact sometimes referred to as point contact. Their tooth surfaces do not stand up under heavy loads, unless the gears are outrageously increased in size. The contact deficiency could in principle be eliminated by cutting the larger member as a wormgear mating with a large helical worm with many threads or teeth. However hobs representing large multi-threaded worms are extremely costly and require long delivery times, if available at all.

One object of the present invention is to remedy this condition, to provide a method and means for accurately producing wormgears to mate with large multithreaded worms, using standard hobs, such as singlethreaded hobs of standard normal pitch. Such hobs can be kept in stock. A further object is to cut the wormgear of any wormgear pair with a standard hob or tool, provided the pair is designed for standard normal pitch. Another aim is to accomplish the above objects without requiring special cams or parts.

A further aim is to more accurately produce crowned hub members of gear couplings of ample adjustability, and to produce on spur and helical gears tooth surfaces eased off adjacent their ends in the hobbing operation. A still further object is to provide gear-producing equipment of wide adaptability, including the production of members with tapered root surface, as exist on conventional gear-shaper cutters.

Other objects will appear in the course of the specification and in the recital of the appended claims.

The invention will be described with the drawings, in which FIGS. 1 to 3 are diagrams explanatory of some principal applications of the method and its means. FIG. 1 refers to the production of a wormgear conjugate to a large helical worm. FIG. 2 refers to the crowning of a gear-coupling hub member. FIG. 3 refers to angularly adjustable gearing, such as described in my U.S. Pat. No. 3,229,541.

FIG. 4 is a diagram similar to FIG. 1, but showing the relative feed motion split up.

FIG. 5 corresponds to FIG. 2 and also shows the feed motion split up in a novel way.

FIGS. 6 and 7 are diagrams showing how the position of the straight-line element of an involute helicoid is determined that contacts a given tangent plane. The cutting edges of a hob of the involute system lie in an involute helicoid, if intended to produce fully conjugate teeth.

FIG. 8 is a diagrammatic and fragmentary axial view of an involute worm, showing the path of contact with the wormgear at various turning positions. FIG. 9 is an enlarged view of a portion of FIG. 8.

FIGS. 10 and 11 are diagrams explanatory of the feed requirements to produce fully conjugate teeth. The two Figures refer to opposite sides of the teeth.

FIG. 12 is a diagram illustrating the contact with the hob thread on a crowned hub member of a gear coupling.

FIG. 13 is a diagrammatic plan view of a machine embodying the invention.

FIG. 14 is a corresponding diagrammatic front view.

FIG. 15 is a fragmentary section taken along lines 15--l5 of FIG. 13.

FIG. 16 is a diagrammatic section and side-view of a hob drive corresponding to FIG. 13 and FIG. 14, the view being taken from the right of FIG. 13.

FIG. 17 is a diagram explanatory of the feed motion of the tool-carrying slide shown in FIGS. 13 and 14.

FIG. 18 is a diagram explanatory of the varying feed motion in the direction of the tooth depth, as derived from a pivoted feed-actuating member that turns at a non-uniform rate.

FIG. 19 is a diagram showing how this same member can be used to produce uniform feed.

FIG. 20 is a diagram showing how backlash may be eliminated in driving said feed-actuating member.

FIG. 21 is a section taken along lines 21-21 of FIG. 20.

FIG. 22 is an axial view of a cam that may be used in place of the eccentric 92 shown in; FIG. 18.

FIG. 23 is a diagrammatic and fragmentary view of a hob drive similar to FIG. 16, but permitting parallel displacement of the hob spindle as an additional feed.

FIG. 24 is a front view thereof, looking as in FIG. 14.

FIG. 25 is a diagram, partly in section, of the member I that controls the parallel displacement of the hob spindie.

In FIG. 1- numeral 30 denotes a wormgear conjugate to a large multi-threaded worm 31 with axis 32. According to the invention wormgear 30 may be cut with a smaller hob 33 that has a single thread or fewer threads than the worm, by feeding the hob about the worm axis 32 while changing the timing accordingly. The invention provides means for increasing the mathematical accuracy of this process.

Instead of using a feed motion about axis 32 I may attain the same relative feed by substituting an angular feed about an axis parallel to axis 32 plus a translatory feed motion in a circular path. The axis of the angular feed motion may have a fixed relationship to the tool. The translatory feed motion is preferably made up of two rectilinear components at right angles to each other, one of them being a uniform motion in the direction of the axis of the workspindle and the other a vary ing motion in a direction at right angles thereto. Such linear feed motions are already in use on conventional machines. The invention adds the angular feed motion, the operation of the feed, and furthermore means to increase the mathematical accuracy of the process.

In FIG. 4 the angular feed motion indicated is about an axis 34 perpendicular to the drawing plane and parallel to axis 32. It intersects the axis 35 of the hob 33 that is shown in a position displaced from the central position shown in FIG. 1. The central position of the wormgear is indicated in dotted lines 30. The wormgear has performed a circular translation along an arc 36, so that the center of the wormgear has moved from 37 to 37, while the hob has been tilted through the angle 36' of arc 36, about axis 34.

In FIG. 2 a hub member 40 of a gear coupling is shown crowned with a hob 41 fed about an axis 42. The hob center 43 describes a circular path containing such positions as 43', 43". The hob axis 44 thus assumes different angular positions, such as position 44 at point 43'. This angular tilt is omitted in conventional production, where the hob body performs a circular translation. In principle this introduces an error. It is practically negligible on couplings for small angularities when single-thread hobs are used. It increases however sharply as the shaft angularity increases. It is avoided with feed about axis 42 or about any other axis such as 42', 42".

Here also the feed motion is split up into an angular feed of the hob about an axis 45 and into a translation in two directions of the workpiece. Axis 45 is shown here passing through hob center 43. The workpiece 40 performs a circular translation. Its center point 46 (FIG. moves to positions such as 46, 46". These can be obtained by displacing the whole system, hob and hub, in parallel position from point 43 of FIG. 2 to point 43 and again from point 43 to point 43. This results in the set-up shown in FIG. 5. The connecting lines 4343 and 4646 (FIG. 5) have the same length and inclination; and the connecting lines 43"43 and 46-46" also. The locus of the points 46, 46', 46" is a circular arc of the same radius as the circular arc on which points 43, 43, 43" lie.

The adjustable gearing shown in FIG. 3 contains a gear 47 corresponding to wormgear of FIG. 1, and a crowned gear 48 corresponding to hub 40 of FIG. 2.

Diagram FIG. 8 illustrates the mesh of involute helical worm 31 shown in FIG. 1 with its wormgear, at a larger scale. The drawing plane contains the axis of the wormgear and is perpendicular to the worm axis 32. The profiles of the worm threads or teeth are involutes of a circle, as those of conventional gear teeth. The involute helical tooth surfaces have a cylindrical base surface 50; and they contain straight-line elements tangent to helices of the base cylinder. The surface normals 51, or surface perpendiculars, are also tangent to the base cylinder. They also have a constant inclination to the drawing plane of FIG. 8 and are inclined thereto at the base-helix angle. The latter is the complement of the lead angle on the base cylinder.

As the helical worm or pinion meshes with the wormgear in the same way when it turns on its axis in a fixed axial position and when it moves along its axis without turning, in a rack motion, the surface normals at points of contact intersect the instant axis 52 of said rack motion. It passes through pitch point 53 and is parallel to the wormgear axis, lying in the drawing plane. The surface of action between worm 31 and wormgear 30 contains all the surface normals 51 passing through axis 52.

At pitch point 53 the surface normal of the hob thread matches the surface normal of the wormgear pair. As the hob is fed about the worm axis 32 the same surface normal of the hob thread intersects the drawing plane at points 53, 53" etc. of circle 54 that is centered on worm axis 32, while the contact normals intersect the drawing plane on axis 52. Looking at the portion around point 53", shown in enlargement in FIG. 9, the surface normal 51 of the hob thread passes through point 53" while the equally directed contact normal passes through point 53i of axis 52. It intersects the tangent plane of the hob thread at point 55.

The involute helical hob thread contacts said tangent plane along a straight-line element 56. Full mathematical accuracy is attained when the hob is shifted along its tangent plane so that line 56 passes through point 55. This shift 55'55 is preferably made along the helix tangent at point 53".

Mathematical computation is presented later on.

The shift may be a continuous or stepwise nonuniform motion that reverses at pitch point 53. This feed motion is in opposite directions on opposite sides of the teeth. When using this shift-feed opposite sides of the teeth have to be cut successively.

When the shift is omitted the wormgear teeth produced are eased off adjacent their tooth ends from fully conjugate shape. While some ease-off or crowning is desirable, it can be overdone. It should be under control, and the present invention provides such control. It lets us produce the fully conjugate shape or any deliberate departure therefrom.

The method requires a hob of smaller diameter than the worm.

FIG. 12 illustrates hobbing a crowned hub member of a gear coupling. Here the teeth lie in axial planes. Crowning is shown about a center 42. The desired surface normals appear in projection as radial lines, such as line 42-43" if the'face width were extended. The straight-line elements of opposite involute helical thread sides appear here equally and oppositely inclined from radial line 42-43. Lack of shift here decreases the ease-off, at least in principle. As the decrease is very small and practically equal on both sides of the teeth, it is unnecessary to provide a shift in this application. The use of the added angular hob feed is sufficient for high accuracy.

APPROXIMATE METHODS OF I-IOBBING WORMGEARS The simplest approximation is omitting the described varying rate translatory displacement or shift of the hob. Relatively small hobs should then be used, as they minimize the departure from the full conjugacy.

The ease-off produced thereby is confined strictly to the regions adjacent the tooth ends. It might be called an ease-off of the fourth and higher orders, increasing with the fourth and higher power of the distance from the tooth middle.

A still closer approximation can be had by decreasing the cutting depth very slightly immediately adjacent the tooth ends, as will be further gone into later on. These approximate methods can cut both sides of the teeth simultaneously.

While the invention has been particularly described as applied to wormgears, it is equally applicable to hour-glass type enveloping worms that are conjugate to helical gears.

It applies moreover also to non-involute tooth shapes.

STRUCTURE The design diagrammatically illustrated in FIGS. 13 to 15 comprises a work spindle containing a drive gear 64 and workpiece 65, rotatably mounted on work slide 66. This slide is movable in the direction of the axis 67 of the work spindle at a uniform rate by such conventional means as a screw and nut 70.

The tool head 71 contains a tool spindle mounting a hob 72 or other tool that has working portions projecting outwardly from a generally cylindrical body and inclined to the peripheral direction of the tool. The tool spindle is carried by a swivel plate 71 that is adjustable in the tool head about an axis 73. Axis 73 intersects the tool-spindle axis at right angles. The whole tool head 71 is pivoted on an axis 74 that in the instance illustrated in FIG. 13 passes through the working portion of the hob, at the cutting engagement. This position renders inaccuracies in the angular feed motion least effective. Tool head 71 with pivot axis 74 is mounted on a slide 75 movable on the machine frame in a direction at right angles to work axis 67.

The hob drive is further shown in FIG. 16. An electric motor 76 (FIG. 14) mounted on the tool head drives a miter gear 77 (FIG. 16) that is coaxial with adjustment axis 73, for instance through change gears, a belt and a pulley 78, Miter gear 77 rotates the tool spindle through miter gear 79 and a gear pair 80, all mounted on swivel plate 71'. Miter gear 77 also transmits motion to the work spindle through miter gear 81 and a pair of helical gears 82, 82 mounted directly on the tool head. Gear 82' is coaxial with the pivot axis 74.

FIG. 16 shows a design that renders the work rotation, the timing, independent of the angular feed motion of the tool head.

Helical gear 82 is rigid with a shaft 83 that contains a helically splined end 83. End 83' engages the hub of miter gear 81 that is mounted in an axially fixed position. A tapered roller 84 is mounted on shaft 83 in a position axially fixed to the shaft. It engages an internal helical way of an arcuate portion 85 that is maintained rigid with slide 75 and does not turn with the tool head. Because the angular feed of the tool head is at most one sixth of a full turn, portion 85 may be supported through openings in said tool head.

As the tool head turns on axis 74 the roller 84 moves along said helical way and causes shaft 83 to move axially, thereby additionally turning shaft 83 and with it gear 82. If it were not for the axial motion of shaft 83, gear 82' would be additionally rotated through the angle of the angular feed. And it would transmit additional turning motion to the workpiece. This additional motion is avoided by using a lead and hand of said helical way such that the additional motion is cancelled.

If straight spur teeth were used on gears 82, 82' the axial displacement of shaft 83 should be such that at hob stand-still the helical splines at 83' turn gear 82 so that it rolls on gear 82' maintained stationary. The use of helical teeth on gears 82, 82 affects the selection of the leads in known manner.

THE PIVOTED FEED-ACTUATING MEMBER The varying feed of slide 75 and the angular feed of the tool head are actuated by a novel pivoted feed member 86 here mounted on slide 75. While it could be combined with the tool head, I preferably place it further back on slide 75 for better access. It appears in FIG. 13 and in section in FIG. 15.

A screw 87 (FIG. turns in proportion to feed screw 68 that operates the feed along the axis of the work spindle. It displaces a slide member 88 movably mounted on slide 75, and reverses its motion or reversal of said feed. Slide member 88 contains a straight way 89 extending at right angles to screw 87. It is shown here engaged by a sliding block pivoted on a pin 90 projecting from feed-actuating member 86. The latter is journalled on slide 75, pivoting about an axis 91. Uniform displacement of slide member 88 on slide turns member 86. It turns it at a non-uniform rate that is a minimum in the central position shown in FIG. 13.

If its turning angle from central position is denoted 0, it will be seen that sin 0 is proportional to the uniform displacement of slide member 88 on slide 75, as measured from the central position shown in FIG. 13. It is also proportional to the feed in the direction of the axis of the work spindle.

It is understood that an enlarged pin could also be used without the sliding block, if desired.

The feed-actuating member 86 carries on top an eccentric 92 without or with a sliding block, engaging a way 93 of a part 94 rigid with and adjustable on the machine frame. Part 94 is shown in dotted lines in FIG. 15. Eccentric 92 operates the varying feed at right angles to the direction of the axis of the work spindle. It is radially adjustable on member 86 along ways 86'.

The angular feed motion of the tool head 71 is identical with the motion of actuating member 86 and is transmitted with parallel linkage through arm 95.

The action of member 86 will be further described with FIGS. 17 to 19. FIG. 17 left shows axis 91 and the axes 90, 92' of pin 90 and eccentric 92 respectively, and the feed displacement 96 relatively to slide 75. FIG. 17 right illustrates the feed displacement of slide 75 with respect to the stationary way that extends along line 97. The displacement is the same, but in opposite direction.

FIG. 18 further shows the displacement relatively to slide 75 in a position away from the central position shown in FIG. 13. The feed-actuating member 86 is pivoted at 91 and shown dotted. Slide member 88' 0perates the turning motion of member 86 in the same way as member 88 shown in FIG. 13.

A principal merit of this feed-actuating member is that it attains a true circular translation in combination with uniform feed along the work-spindle axis, and that the radius of the true circular path can be changed by radially adjusting eccentric 92.

The retention of the uniform feed axially of the workpiece extends the range of the machine to the production of spur gears and helical gears. These can be readily hobbed with any desired degree of crowning by setting eccentric 92 close to the axis 91. For this minute kind of crowning no angular feed need be provided on the tool head 71.

FIG. 19 shows how tapered teeth can be produced with member 86, such as exist for instance on gearshaper cutters. A uniform feed of slide 75 is added to the uniform feed lengthwise of the axis of the workpiece. This may be done with an eccentric 99 offset laterally a fixed distance from axis 91. It can be left in place if part 94 with way 93 can also be laterally displaced, as shown in FIG. 19. Eccentric 92 is set to zero eccentricity when using eccentric 99. Different rates of radial feed are attained by gearing screw 87 to a different turning rate.

FIGS. 20 and 21 show a way to eliminate backlash in driving the feed-actuating member 86 through slide member 88'. A roller 90, is mounted on pin 90, with plain or needle bearings. The roller engages one side of way 89. On the opposite side it bears against a somewhat resilient roller 100 held in place by a cage 101.

The resilient roller is preloaded and engages the opposite side of way 89'.

FIG. 22 shows a cam 102 that may be used in place of eccentric 92 in hobbing wormgears, shown at a larger scale. It reduces the ease-off or crowning adjacent the very tooth ends. Cam profile 103 is part of an ellipse whose curvature center on the minor axis coincides with the center 92' of eccentric 92. The opposite profile 103' has a constant distance from profile 103 between parallel lines, to fit the width of way 93 in all turning positions.

A set of cams 102 may be carried in stock to accommodate various jobs. Other cams may be substituted for other purposes.

FIGS. 23 and 24 fragmentarily show a hob drive for lateral hob feed, preferably in the direction of the helix tangent at the point of engagement. The gear 106 drives the hob spindle through a parallel shaft coupling 107 of known type, that permits lateral displacement of the hob spindle and some axial displacement. The hob is journalled on slide-part 108 that is movable axially of the hob spindle on a slide-part 110. The latter is movable at right angles thereto on swivel plate 71". Slidepart 108 is shown in dotted lines in FIG. 24. A plate 111 contains a straight slot 112 shown dotted in FIG. 24. The slot direction can be set to the lead angle of the hob thread by angularly adjusting plate 111 about an axis that has the same direction as adjustment axis 73. Slot 112 is engaged by a roller 113 mounted on a central projection of slide-part 108.

It constrains the slide-part 108 with hob to move in the direction of the helix tangent.

Motion is applied to slide-part 110, as by means of a screw, whose turning motion is remotely controlled.

MATHEMATICAL TREATMENT for the embodiment described with FIGS. 23 and 24.

Let a few basic concepts be repeated. We start out with a normal pitch vr-M, as measured on the pitch surface of the worm developed into a plane. Let R denote the pitch radius, n the number of threads, e the normal pressure angle or profile inclination in the normal plane. The lead angle s of either the worm or hob thread is then sin s M'n/2 R The transverse pressure angle 2, of the helicoid is tan e, tan e/sin s The radius c of the base circle is c R'cos e,

And the lead angle s,, at the base cylinder is tan s tan s/cos e,

The above symbols may be used without subscript for the worm and with subscript h for the hob.

Let us now consider the contact line of the hob thread with its tangent plane. FIG. 6 is a view of the pitch plane that contains line 52 (FIGS. 6, 8) and is parallel to the worm axis 32. The helix tangent at point 53 includes an angle s with line 52. The projected hob axis 57 is inclined at an angle s to the projected surface normal 58. The direction of the sought contact line is obtainable by projecting a point 60 of projected hob axis 57 to the tangent plane at 53, obtaining point 61. The connecting line 53-61 is the contact line between the continuous hob thread and the tangent plane. FIG. 7 shows this contact line viewed in the direction of the worm axis 32. It includes an angle 14 with the vertical, that is with radial line 62. Angle u can be computed with the formula tan u cos s/sin e-cos 2 tan s tan s-sin e) as can be demonstrated mathematically.

At point 53 the normal, as viewed in FIG. 8, in inclined at an angle e, to line 52, while at point 53" it is inclined at an angle (e, 0) thereto, 9 being the turning angle 53-32-53". Hence, with R 32-53, the distance 53"53 amounts to R(l cos 0)/sin(e, 0)

As the tangent plane is inclined at an angle s to the plane of FIGS. 8 and 9, the projected distance 53"-55 appears as (53"53,)'cos s Angle 5553"-55' (FIG. 9) is e, u) and angle 55-5553" is (90+ u). Hence, the shift 55-55, as seen in FIG. 9, amounts to (53"55) [cos(e, u)/cos u and the shift sh along the helix tangent of the hob amounts to The portion within brackets is constant for all turning positions, for all angles 0. Let it be denoted R.

FIGS. 10 and 11 illustrate the nature of the shift for opposite tooth sides. Circles 150, have each a radius R, as above defined. They are centered at 151, 151' respectively. Their points 153, 153' correspond to generation at pitch point 53, that is to the central position of the generating motion. Circles 154, 154 have each a radius R"cos e The shift is represented by the varying distance 155-156 and 155'-156' respectively on the tangents to circles 154, 154.

FIG. 25 indicates a way of controlling this hob feed with a servo-mechanism. A plunger is axially movable without turning in a sleeve 161. Sleeve 161 is secured to a table fed about axis 151 shown also in FIG. 10. Plunger 160 has a ball-end centered at 164, engaging a straight way of matching circular arcuate profile. The plunger and sleeve are shown in the central position of feed, when ball center 164 coincides with point 153 of FIG. 10. They are adjusted to angle e, also shown in FIG. 10.

Plunger 160 is pressed towards way 165 for instance by oil introduced under some pressure through opening 166. As the table turns on its axis 151 the ball end of the plunger follows the center line 165' of way 165.

A screw engages the center of the plunger. It is rigid with a gear 171 rotatable in sleeve 161 and axially fixed thereto. A small electroc motor (not shown) operates gear 171 and screw 170. It is controlled by contact between the plunger and its way. As the table turns on center 151 away from the central position contact of the ball-end is made to shut off current to said motor. The motor turns until contact is established and then stops.

A similar electric motor duplicates the motion of the motor on said table and operates the screw 114 shown in FIG. 24.

The opposite sides of the teeth may be cut in the return feed after angularly switching the control unit so that the center line 168 of the plunger appears at 168 in the central position, with appropriate control change. A set-over should also be made between cutting opposite sides of the teeth, to widen the tooth space cut. The hob thread should be somewhat narrower than the width of the tooth spaces. The set-over may be made by additionally turning the workpiece.

The complete operation with forward and return feed may be done automatically, if desired.

In place of the structure described with FIG. 25, any other suitable known form of remote control may be used.

While the invention has been described with several different embodiments thereof, it will be understood that it is capable of further modification, and this application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice in the art to which the invention pertains, and as may be applied to the essential features hereinbefore set forth, and as fall within the scope of the invention or the limits of the appended claims.

I claim:

1. The method of generating gear-tooth surfaces, which comprises providing a tool having working portions projecting outwardly from a generally cylindrical body, said portions being inclined to the peripheral direction of the tool,

rotating said tool and a workpiece in timed relation on their respective axes,

effecting relative bodily feed motion between said tool and workpiece in the direction of the axis of the workpiece and relative bodily feed motion in a direction at right angles thereto,

and effecting relative angular feed motion between said tool and workpiece about an axis at least approximately at right angles to the direction of the axis of the workpiece.

2. The method according to claim 1, wherein the feed motion in the direction of the axis of the workpiece is effected at a uniform rate.

3. The method according to claim 1, wherein said tool is a hob, having a plurality of cutting teeth arranged in a helical thread.

4. The method according to claim 1, wherein an additional relative translatory motion is effected between the tool and workpiece, said additional motion is at a varying rate, reversing between opposite ends of the generating cycle.

5. The method according to claim 4, wherein said additional motion is a parallel displacement of the tool axis.

6. In a machine for generating tooth surfaces on a rotating workpiece with a rotating tool having working portions at an angle to its peripheral direction, said machine containing means for positively timing the tool rotation to the rotation of said workpiece, the combination of a tool head,

a tool spindle rotatably mounted. in said tool head,

said tool spindle being angularly adjustable in said tool head about an axis intersecting the axis of the tool spindle,

means for effecting uniform feed motion between said tool head and workpiece in the direction of the axis of the workpiece, means for effecting varying feed motion in a generally radial direction at right angles to the axis of the workpiece in time with said uniform feed motion,

and means for angularly feeding the tool head about an axis inclined to the direction of the tool axis and at least approximately at right angles to the direction of the axis of the workpiece.

7. In a machine according to claim 6, wherein the axis of angular feed of the tool head intersects said adjustment axis at right angles.

8. In a machine according to claim 6,

a pivoted feed-actuating member,

means for turning saidfeed member on its axis at a non-uniform rate as compared with said uniform feed motion and for reversing its turning motion on reversal of said uniform feed motion,

said rate being a minimum intermediate the ends of the generating cycle.

9. The combination according to claim 8, wherein the sine of the turning angle 6, (:sin 0), of the feedactuating member is in direct proportion to the feed in the direction of the axis of the work spindle, the turning angle 0 being measured from a mid-position of feed.

10. The combination according to claim 8, wherein the feed-actuating member contains a part radially adjustable thereon.

11. The combination according to claim 8, wherein the feed-actuating member contains a part radially adjustable thereon, said part engages a plane-sided abutment.

12. The combination according to claim 10, wherein said adjustable part contains a cylindrical projection that extends parallel to the axis of said feed-actuating member.

13. The combination according to claim 10, wherein said adjustable part is a cam.

14. The combination according to claim 10, wherein said adjustable part is a disk-type cam whose contour crosses the radius of adjustment at right angles. 

1. The method of generating gear-tooth surfaces, which comprises providing a tool having working portions projecting outwardly from a generally cylindrical body, said portions being inclined to the peripheral direction of the tool, rotating said tool and a workpiece in timed relation on their respective axes, effecting relative bodily feed motion between said tool and workpiece in the direction of the axis of the workpiece and relative bodily feed motion in a direction at right angles thereto, and effecting relative angular feed motion between said tool and workpiece about an axis at least approximately at right angles to the direction of the axis of the workpiece.
 2. The method according to claim 1, wherein the feed motion in the direction of the axis of the workpiece is effected at a uniform rate.
 3. The method according to claim 1, wherein said tool is a hob, having a plurality of cutting teeth arranged in a helical thread.
 4. The method according to claim 1, wherein an additional relative translatory motion is effected between the tool and workpiece, said additional motion is at a varying rate, reversing between opposite ends of the generating cycle.
 5. The method according to claim 4, wherein said additional motion is a parallel displacement of the tool axis.
 6. In a machine for generating tooth surfaces on a rotating workpiece with a rotating tool having working portions at an angle to its peripheral direction, said machine containing means for positively timing the tool rotation to the rotation of said workpiece, the combination of a tool head, a tool spindle rotatably mounted in said tool head, said tool spindle being angularly adjustable in said tool head about an axis intersecting the axis of the tool spindle, means for effecting uniform feed motion between said tool head and workpiece in the direction of the axis of the workpiece, means for effecting varying feed motion in a generally radial direction at right angles to the axis of the workpiece in time with said uniform feed motion, and means for angularly feeding the tool head about an axis inclined to the direction of the tool axis and at least approximately at right angles to the direction of the axis of the workpiece.
 7. In a machine according to claim 6, wherein the axis of angular feed of the tool head intersects said adjustment axis at right angles.
 8. In a machine according to clAim 6, a pivoted feed-actuating member, means for turning said feed member on its axis at a non-uniform rate as compared with said uniform feed motion and for reversing its turning motion on reversal of said uniform feed motion, said rate being a minimum intermediate the ends of the generating cycle.
 9. The combination according to claim 8, wherein the sine of the turning angle theta , (sin theta ), of the feed-actuating member is in direct proportion to the feed in the direction of the axis of the work spindle, the turning angle theta being measured from a mid-position of feed.
 10. The combination according to claim 8, wherein the feed-actuating member contains a part radially adjustable thereon.
 11. The combination according to claim 8, wherein the feed-actuating member contains a part radially adjustable thereon, said part engages a plane-sided abutment.
 12. The combination according to claim 10, wherein said adjustable part contains a cylindrical projection that extends parallel to the axis of said feed-actuating member.
 13. The combination according to claim 10, wherein said adjustable part is a cam.
 14. The combination according to claim 10, wherein said adjustable part is a disk-type cam whose contour crosses the radius of adjustment at right angles. 